The Universe is Flat

Another outlandish conclusion from the flat-earthers?


Something that looks like a sphere, made up of straight lines. (Source: me. I generated this in Wolfram Mathematica)


When you see the Earth from only the perspective of your eyes, you don’t see a curved Earth explicitly. Of course, I’m not suggesting the Earth is globally flat. There are mountains of evidence proving the globe model, but in your general vicinity, the horizon is a straight line. You perceive the local area you’re in as flat land. Flat Earth is a good approximation for if you’re only referring to a (very) small region.

The key point of this is that an infinitely many locally flat places can be added together to have a globally curved plane. You change the angle of your path by a tiny amount an infinite number of times as you move along a surface. Suddenly, your surface is curved to an outside observer.

A consequence of this is that locally straight lines are not globally straight lines. When you move in a straight line along the Earth’s surface while constantly keeping an eye on your compass to make sure your path is straight, you’re actually going on a curved path when seen from the International Space Station.


File:End of universe.jpg

Straight lines in a curved universe. As you can see, even if you travel along the locally straight paths marked out by the white grid, your overall global path is not straight when there is curvature. Credit: NASA, image in public domain. NASA copyright policy.


What does that have to do with the price of eggs?

Eggs are curved. Why isn’t the universe?


What’s nontrivial is the global flatness of the universe. According to observations from probes orbiting the Earth, the Universe is (mostly) globally flat. If any curvature existed, it would be at most 1 part in 10,000, i.e. tiny. Straight lines in any part of the universe appear flat from outside the universe (not that such an outside exists in our current understanding of physics.)

In space, general relativity is what causes the universe to bend into curved paths, just like the ones on the surface of the Earth. Mass tells spacetime how to bend, and spacetime tells mass how to move. It’s not just mass though that can bend spacetime, but energy as well.

The problem is thus: the universe is too flat. Our models tell us that to have a universe this exceedingly flat, some numbers have to be tuned in a very specific way.


The Mass Density Parameter

It was said that you would bring balance to the universe, not leave it in darkness!


Most important of all is the mass and energy density of the universe. The universe has a critical density where flatness is possible. It turns out that when you use probes to measure the density of all mass and energy in the universe, it almost exactly adds to this critical density.

As the universe expands, this energy density fluctuates away from the critical density of the universe. This means in the early universe, the density parameter was even more finely tuned to the critical density of the universe, at most deviating 1 part in 1062. This is an absurd level of accuracy for any experiment known to man. Changing the mass-energy density even by a small amount is extremely consequential to the universe’s evolution. There’s 13.7 billion years of its history after all. It thus makes you wonder, does the universe have its own intentions after all?


Inflation Theory

The theory of inflation is a pathway to many phenomena some consider to be unnatural


Cosmologists have come up with a possible explanation for the problem. They posit that there was a very early period in the universe less than 10-30 seconds after the big bang where the universe expanded by a factor 1026. Quite a thought. It is currently the accepted explanation, but there has been no evidence so far to suggest such an inflation occurred as of yet (in fact there has been little evidence of any kind from that far back).

It’s very difficult to look that far into the early universe because the oldest things we can see are also the furthest away things in the universe. We haven’t even seen anything before hundreds of millions of years after the big bang. As we improve our telescopes (fingers crossed, JWST), we should gain new insights into this very early period, but it will be a while before we know for sure. Cosmologists are smart. They’ll figure something out.

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